Zhurnal Matematicheskoi Fiziki, Analiza, Geometrii [Journal of Mathematical Physics, Analysis, Geometry]
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Zhurnal Matematicheskoi Fiziki, Analiza, Geometrii [Journal of Mathematical Physics, Analysis, Geometry], 2014, Volume 10, Number 1, Pages 3–43
DOI: https://doi.org/10.15407/mag10.01.003 (Mi jmag582) 		 
This article is cited in 13 scientific papers (total in 13 papers)

The Two-Phase Hele–Shaw Problem with a Nonregular Initial Interface and Without Surface Tension

B. V. Bazaliy, N. Vasylyeva

Institute of Applied Mathematics and Mechanics, 74 R. Luxemburg Str., Donetsk 83114, Ukraine
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DOI: https://doi.org/10.15407/mag10.01.003
Abstract: In the paper, we consider the two-dimensional Muskat problem without surface tension on a free boundary. The initial shape of the unknown interface has a corner point. We prove that the problem has a unique solution in the weighted Hölder classes locally in time and specify the sufficient conditions for the existence of the "waiting time" phenomenon.
Key words and phrases: Laplace equation, free boundary problems, Muskat problem, weighted Hölder spaces, waiting time property.
Received: 06.11.2012
Revised: 28.05.2013
Bibliographic databases:
Document Type: Article
MSC: Primary 35R35; Secondary 35J25, 35B65
Language: English
Citation: B. V. Bazaliy, N. Vasylyeva, “The Two-Phase Hele–Shaw Problem with a Nonregular Initial Interface and Without Surface Tension”, Zh. Mat. Fiz. Anal. Geom., 10:1 (2014), 3–43
Citation in format AMSBIB
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\by B.~V.~Bazaliy, N.~Vasylyeva
\paper The Two-Phase Hele--Shaw Problem with a Nonregular Initial Interface and Without Surface Tension
\jour Zh. Mat. Fiz. Anal. Geom.
\yr 2014
\vol 10
\issue 1
\pages 3--43
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\crossref{https://doi.org/10.15407/mag10.01.003}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3236960}
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    • This publication is cited in the following 13 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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